11.2.5 problem 12

Internal problem ID [1476]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 4.2, Higher order linear differential equations. Constant coefficients. page 180
Problem number : 12
Date solved : Monday, January 27, 2025 at 04:57:47 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(y(x),x$6)-3*diff(y(x),x$4)+3*diff(y(x),x$2)-y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_6 \,x^{2}+c_5 x +c_4 \right ) {\mathrm e}^{-x}+{\mathrm e}^{x} \left (c_3 \,x^{2}+c_2 x +c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 50

DSolve[D[y[x],{x,6}]-3*D[y[x],{x,4}]+3*D[y[x],{x,2}]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (x^2 \left (c_6 e^{2 x}+c_3\right )+x \left (c_5 e^{2 x}+c_2\right )+c_4 e^{2 x}+c_1\right ) \]